Common fixed point theorems for mappings satisfying E.A property

Abstract

The present dissertation entitled, “COMMON FIXED POINT THEOREMS FOR MAPPINGS SATISFYING E.A PROPERTY”, embodies a brief account of investigations carried out by various authors on existence of fixed points of self-mappings in metric spaces under the supervision of Dr. S.S. Bhatia, Professor, School of Mathematics and computer Applications, Thapar University, Patiala. The aim of this work is to study some results on existence and uniqueness of common fixed points using E.A property. Fixed point theory is a major branch of non-linear functional analysis because of its wide applicability. Various problems in physics, chemistry, biology, economics etc. can be solved by making use of fixed point theorems. The work presented in this dissertation has been divided into four chapters. The first chapter is introductory. In this chapter, we present a brief account of basic definitions and results which will be used in the later chapters. In second chapter, we present the Banach fixed point theorem and some other fixed point theorems. Also, we present one of its application to solve a differential equation. Towards the end of this chapter, we have studied the Caristi’s fixed point theorem [3]. The purpose of the third chapter is to study an interesting property called E.A property introduced by Aamri and Moutawakil [1]. Also, we have studied some common fixed point theorems under strict contractive conditions for mappings satisfying E.A property. In the fourth chapter, we have studied the results given by Imdad, M. and Ali, J. in [7]. The purpose of this chapter is to study how the E.A property replaces the containment condition of ranges of one mapping into the range of other in common fixed point considerations up to a pair of mappings. References of different publications cited in the present dissertation have been given